Semi-Riemannian Geometry with Nonholonomic Constraints

Abstract

In the present article the geometry of semi-Riemannian manifolds with nonholonomic constraints is studied. These manifolds can be considered as analogues to the sub-Riemannian manifolds, where the positive definite metric is substituted by a nondegenerate metric. We study properties of the exponential map, the Christoffel symbols and other differential operators are introduced. We study solutions of the Hamiltonian system and their projections into the underlying manifold. The explicit formulae were found for a specific example of a semi-Riemannian manifold with nonholonomic constraints.